Explore the vast range of titles available.

Bayesian information criterion (BIC) is known to identify the true model consistently as long as the predictor dimension is finite. Recently, its moderate modifications have been shown to be consistent in model selection even when the number of variables diverges. Those works have been done mostly in mean regression, but rarely in quantile regression. The best-known results about BIC for quantile regression are for linear models with a fixed number of variables. In this article, we investigate how BIC can be adapted to high-dimensional linear quantile regression and show that a modified BIC is consistent in model selection when the number of variables diverges as the sample size increases. We also discuss how it can be used for choosing the regularization parameters of penalized approaches that are designed to conduct variable selection and shrinkage estimation simultaneously. Moreover, we extend the results to structured nonparametric quantile models with a diverging number of covariates. We illustrate our theoretical results via some simulated examples and a real data analysis on human eye disease. Supplementary materials for this article are available online.

In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parameterization that characterizes any collection of noncrossing quantile planes over arbitrarily shaped convex predictor domains in any dimension by means of unconstrained scalar, vector and function valued parameters. Statistical models based on this parameterization inherit a fast computation of the likelihood function, enabling penalized likelihood or Bayesian approaches to model fitting. We introduce a complete Bayesian methodology by using Gaussian process prior distributions on the function valued parameters and develop a robust and efficient Markov chain Monte Carlo parameter estimation. The resulting method is shown to offer posterior consistency under mild tail and regularity conditions. We present several illustrative examples where the new method is compared against existing approaches and is found to offer better accuracy, coverage and model fit. Supplementary materials for this article are available online.

Questions: In drylands above-ground net primary production (ANPP) and rain-use efficiency (RUE) are common ecological indicators for assessing ecosystem state, including degradation and supply of key ecosystem services. However, both indicators have been criticized as 'lumped' parameters, since they aggregate complex information. Their value as ecological parameters in decision-making and their use in ecological modelling therefore have been challenged and their explanatory power remains unclear. Furthermore, there is no consensus about the response of ANPP and RUE along precipitation gradients. Methods: Taking advantage of several long-term studies in (semi-)arid environments where ANPP and RUE were recorded, we compiled a data set of 923 yr. We used meta-analysis to disentangle the effects of different ecological layers (climate, soil and land use) on ANPP and RUE. Linear piece-wise quantile regression (LPQR) was used to analyse the response of maximum and median ANPP and RUE as functions of precipitation. We assumed that looking at maximum response (instead of 'average' response) stratified for land-use intensity was an ecologically more plausible way to understand ANPP constrained by precipitation and land use. Results: We separated the impact of different environmental factors into distinct, quantitative effect sizes with the aid of meta-analyses. ANPP was affected by recent and previous precipitation, land use, soil and biome. LPQR revealed that both parameters displayed several sequential linear intersects, which together formed a unimodal trend, peaking around precipitation of 200 mm yr -1 . Unimodal response was more pronounced for maximum values (ANPP max , RUE max ) than for median values. Peak ANPP max and RUE max , as well as post-peak decline (>200 mm yr -1 ) were affected by land use: higher land-use intensity decreased intercepts and increases post-peak decline. Conclusions: Our results have important consequences for the use of RUE as an ecosystem indicator and a tool in ecosystem monitoring and decision-making. Most importantly, grasslands, shrublands and savannas significantly differ in their primary production, with a biome-specific importance of precipitation, land use and previous year's precipitation. We thus propose to establish biome-specific reference values of maximum and average RUE. Our study also contributes to reconcile contradictory findings for ANPP and RUE response along precipitation gradients of varying length.

Quantile regression estimators at a fixed quantile level rely mainly on a small subset of the observed data. As a result, efforts have been made to construct simultaneous estimations at multiple quantile levels in order to take full advantage of all observations and to improve the estimation efficiency. We propose a novel approach that links multiple linear quantile models by imposing a condition on the rank of the matrix formed by all of the regression parameters. This approach resembles a reduced-rank regression, but also shares similarities with the dimension-reduction modeling. We develop estimation and inference tools for such models and examine their optimality in terms of the asymptotic estimation variance. We use simulation experiments to examine the numerical performance of the proposed procedure, and a data example to further illustrate the method.

Aiming to estimate extreme precipitation forecast quantiles, we propose a nonparametric regression model that features a constant extreme value index. Using local linear quantile regression and an extrapolation technique from extreme value theory, we develop an estimator for conditional quantiles corresponding to extreme high probability levels. We establish uniform consistency and asymptotic normality of the estimators. In a simulation study, we examine the performance of our estimator on finite samples in comparison with a method assuming linear quantiles. On a precipitation data set in the Netherlands, these estimators have greater predictive skill compared to the upper member of ensemble forecasts provided by a numerical weather prediction model.

Studies on probabilistic demand forecasting remain relatively limited compared with point forecasting, despite it being especially valuable for operational and planning purposes. This paper demonstrates different applications of probabilistic forecasting in demand response, together with Physical-Based Load Models. The first application shows how to determine the percentage of uncertainty potentially covered by demand response throughout a day, whereas the second application deals with obtaining the number of consumers that would be needed in demand response actions for a desired percentage of coverage. Finally, in the third application, a specific hourly strategy is proposed for demand response policies. These applications facilitate the aggregator’s energy purchasing in the market and the planning of subsequent consumption adjustments through demand response to minimize deviations from the purchased energy. The approach is illustrated using hourly demand data from a small Spanish city, and two machine learning methods were used to produce a set of probabilistic forecasts and compare results: Linear Quantile Regression and a Quantile Regression Forest. Main results show a significant reduction in deviations from the purchased energy after applying the proposed strategy, especially in the case of the forecasting method being less accurate (40.95% and 33.62% of reduction, respectively).

This study examines the estimation of extreme conditional quantiles for distributions with Weibull-type tails. We propose two families of estimators for the Weibull tail-coefficient, and construct an extrapolation estimator for the extreme conditional quantiles based on a quantile regression and extreme value theory. The asymptotic results of the proposed estimators are established. This work fills a gap in the literature on extreme quantile regressions, where many important Weibull-type distributions are excluded by the assumed strong conditions. A simulation study shows that the proposed extrapolation method provides estimations of the conditional quantiles of extreme orders that are more efficient and stable than those of the conventional method. The practical value of the proposed method is demonstrated through an analysis of extremely high birth weights.

Subsampling techniques are efficient methods for handling big data. Quite a few optimal sampling methods have been developed for parametric models in which the loss functions are differentiable with respect to parameters. However, they do not apply to quantile regression (QR) models as the involved check function is not differentiable. To circumvent the non-differentiability problem, we consider directly estimating the linear QR coefficient by minimizing the Hansen–Hurwitz estimator of the usual loss function for QR. We establish the asymptotic normality of the resulting estimator under a generic sampling method, and then develop optimal subsampling methods for linear QR. In particular, we propose a one-stage subsampling method, which depends only on the lengths of covariates, and a two-stage subsampling method, which is a combination of the one-stage sampling and the ideal optimal subsampling methods. Our simulation and real data based simulation studies show that the two recommended sampling methods always outperform simple random sampling in terms of mean square error, whether the linear QR model is valid or not. Les techniques de sous-échantillonnage offrent une approche efficace pour gérer les mégadonnées. Bon nombre de méthodes d’échantillonnage optimales ont été développées pour les modèles paramétriques avec une fonction de perte différentiable par rapport aux paramètres. Elles ne s’appliquent toutefois pas aux modèles de régression quantile dont la fonction en crochet n’est pas différentiable. Afin de contourner ce problème, les auteurs considèrent l’estimation directe des coefficients de régression quantile linéaire en minimisant l’estimateur de Hansen-Hurwitz de la fonction de perte habituelle de la régression quantile. Les auteurs établissent la normalité asymptotique des estimateurs résultants sous une méthode d’échantillonnage générique, puis développent des méthodes optimales de sous-échantillonnage pour la régression quantile linéaire. Ils proposent notamment une méthode de sous-échantillonnage à un stade qui dépend seulement de la longueur des covariables, ainsi qu’une méthode de sous-échantillonnage à deux stades qui combine la méthode à un stade avec un sous-échantillonnage optimal idéal. Les auteurs présentent des études de simulation, certaines basées sur des données réelles, qui montrent que les deux méthodes d’échantillonnage recommandées offrent toujours de meilleures performances que l’échantillonnage aléatoire simple en termes d’erreur quadratique moyenne, que le modèle de régression quantile linéaire soit valide ou non.

The stocking and harvesting strategies used in aquaculture have a strong influence on the economic yields, and producers of aquatic species need alternatives that improve culture conditions and production economy. In this study, we used tilapia growth data from construct bioeconomic models to determine the best stocking and harvesting strategies under homogeneous (HM) and heterogeneous (HT) stocking sizes. We considered 180, 195, 210, and 225 days to harvest. Minimum marketable sizes (MMS) (minimum harvestable fish sizes) were defined according to the market as 350, 400, 450, and 500 g. The bioeconomic analysis considered a fixed price and a price that was variable depending on the size of the fish. With an average growth model and fixed price of USD$ 2.24 kg −1 , independent of MMS, the economic results were negative under both HM and HT stocking and for all harvest times. With size-dependent variable pricing, the highest net benefit was generated by the 225-day, 500 g harvesting strategy, with USD$ 5061.91 per tank under HM and USD$ 5220.53 per tank under HT. Using quantile regressions and fixed pricing, the 225-day, 350 g strategy had the highest yield under HM and HT, with USD$ 4323.51 and USD$ 4190.90 per tank, while with variable pricing, the 225-day, 450 g strategy had higher yield in HM and HT, with USD$ 8634.03 per tank and USD$ 8983.26 per tank. Thus, growth modeling using quantile regression to approximate the population distribution suggested that HT stocking and size-dependent variable pricing generate higher yield for tilapia producers.

Lake levels fluctuations are conditioned by seasonal variability, water resources management and climate change. Recent studies have shown that global warming potentially affects the risk of flooding and that the decisive factor for flood events is not temperature, but precipitation characteristics and hydrological conditions. Flood events have numerous impacts on social, economic and environmental aspects depending on how humans have altered lands, natural rivers and lake dynamics. Flood protection measures can cause conflicts with conservation measures and with ecosystem services because natural capital is not considered able to control floods and to contribute control floods and that it can contribute to human health and safety. In this paper we analysed the flood events in Lake Maggiore for return time periods of 3 – 5 – 10 – 25 – 50 – 100 – 250 – 500 years, considering the flood frequency in the last ten years using 1868-2021 as a reference period. We discussed the probability distribution of flood peaks, the correlation and linear regression between the lake level fluctuations and macroinvertebrates occurrence. We also presented lake coasts flood hazard mapping. The probability distribution that better describes the annual peak level is the Gumbel function, while for spring and autumn flood events the better distribution is the Log-Pearson type III. One of the historical flood events in terms of magnitude was in 2000, characterized by a return time of about 50 years. The last flood event in 2020, was characterized by a return period of about 10 years. Considering the seasonal frequency of flood, the autumn magnitude was higher than the spring one, and the differences between seasonal flood events progressively increased. The results suggested a high probability of a flood event every three years and also a forecast of a flood of about 197 m asl (3.14 m above the average lake level) every 10 years. Raising the lake level will affect the reed bed area from 193 m asl, and it will be more effective at 194.5 m (up to a 10% reduction). During flood events, the whole reed bed area is submerged. As regard macroinvertebrates composition and abundance, the first results show significant negative relationships between all sampling stations altogether vs the abundance of Cladotanytarsus sp. (Chironominae) and nearly significant positive relationships between water levels at Magadino vs Pscectrocladius sordidellus (Orthocladiinae) abundances. These few results are perhaps due to the current limited data availability.